Matrix Problem, Correlations

I am sure this is an easy question but not sure where to start:
Currencies A and B have correlation of 0.8 and currencies B and C have correlation of 0.9, what is the least correlation between A and C? The hint says write down the 3x3 correlation and denote x for the correlation bewteen A and C then only the unknown term in is . Since is a correltation matrix it is symmetric and positive definite. So determine the interval so that has eigenvalues >0 provded . So apparently the answer is . Can anyone shed any light on this question, I'm going round in circles but started with this: is this even right?